Heat oven to 450° with a rack set 5 in. from the heat source. Heat oil in a large ovenproof frying pan over high heat.
Sprinkle chicken with salt and pepper. Brown chicken in hot oil on one side, about 4 minutes. Turn chicken over and add chile flakes, garlic, tomatoes, oregano, and olives.
Transfer pan to oven and cook until chicken is cooked through, about 20 minutes. Lay cheese over chicken and bake just until melted and browned, 2 minutes.
Note: Nutritional analysis is per serving.